Questions tagged [steins-phenomenon]

Stein's phenomenon (paradox) states that when three or more parameters are estimated at the same time, there are more accurate estimators than the average over all observations.

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Dominating Positive Part James-Stein

Is dominating Positive Part James Stein estimator when estimating the mean of a multivariate normal of dimension 3 with known variance(all equal) an open problem? If not, what is this estimator ...
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Clarifying a proof of a particular paper on Steins Estimator

I am trying proving result (5.4) of the following paper. Its a paper on Steins estimator on spherically symmetric cases. The doubt is a s follows: Given $$X|\theta\sim \mathcal{N}(\theta,I)$$ ...
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James-Stein Estimator with unequal variances (Ch. 2)

After studying James-Stein estimators for a few weeks and looking at many different sources I am stuck at trying to understand how Efron and Morris calculated the Toxoplasmosis example in their 1975 ...
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Why is the James-Stein estimator called a “shrinkage” estimator?

I have been reading about the James-Stein estimator. It is defined, in this notes, as $$\hat{\theta}=\left(1 - \frac{p-2}{\|X\|^2}\right)X$$ I have read the proof but I don't understand the ...
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When does $\forall p: E_p[f] = E_p[g]$ imply $f = g$?

Let's say $$E_p[f(X)] = E_p[g(X)]$$ for all $p \in S$, where $S$ might be some parametric family of densities, for instance. Under which assumptions on $S$ does this imply $f = g$? I am reading Efron ...
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Unified view on shrinkage: what is the relation (if any) between Stein's paradox, ridge regression, and random effects in mixed models?

Consider the following three phenomena. Stein's paradox: given some data from multivariate normal distribution in $\mathbb R^n, \: n\ge 3$, sample mean is not a very good estimator of the true mean. ...
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James-Stein Estimator with unequal variances

Every statement I find of the James-Stein estimator assumes that the random variables being estimated have the same (and unit) variance. But all of these examples also mention that the JS estimator ...
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When estimating population mean, how can one half of the sample mean have lower risk than the sample mean itself?

I read Efron and Morris (1977) Stein's Paradox in Statistics with interest yesterday and stumbled upon the statement that, if and only if the population mean is close to zero, than the risk (mean ...
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Is there a connection between empirical Bayes and random effects?

I recently happened to read about empirical Bayes (Casella, 1985, An introduction to empirical Bayes data analysis) and it looked a lot like random effects model; in that both have estimates shrunken ...
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Are there any extensions of the James-Stein estimator for the case of dependent variables?

Are there any extensions of the James-Stein estimator for the case of dependent variables? I've done numeric experiments with the James-Stein estimator on correlated normal variables (5-10 variables,...